Question

What is the solution to the system of equations graphed below?

Answer 1

Answer:

(2,4)

Step-by-step explanation:

There are many ways to resolve a system of equations. We will do it by substitution.  

First, we choose one of the equations, whichever we want, and we solve it for one of the variables, again whichever we want.

Then we plug this back into the other equation substituting for the chosen variable and solving for the other.

Let's choose, for example, the first equation y = x+2.

It's already solved for the variable y, so we just have to plug this into the other equation. Where it says y, we will put x+2.

y = 3x-2

x+2 = 3x-2

And now we solve it for the variable x:

First, we add 2 - x on both sides

x+2+2-x = 3x-2+2-x

4 = 3x-x

4 = 2x

Now we divide by 2 on both sides

4/2 = 2x/2

2 = x

We have the value of x, we need to find out the value of y. We know that

y = x+2 and x=2, so y = 2+2 = 4.

Therefore, the solution is (2,4). The first value is the x and the second one the y.

If we see the graphed, we can notice that (2,4) is the intersection of both lines.

Answer 2

The solution is where the lines intersect...and that would be (2,4)